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Practice: Chain Rule
Related Topics
Wize University Calculus 2 Textbook > Multivariable Functions
Chain Rule
5 Activities
Practice: Chain Rule
If
w
=
z
z
y
x
w = z^z y^x
w
=
z
z
y
x
where
x
=
6
u
+
v
x=6u+v
x
=
6
u
+
v
,
y
=
u
v
y=uv
y
=
uv
and
z
=
tan
v
z=\tan v
z
=
tan
v
.
How many terms in
∂
w
∂
u
\displaystyle \frac{\partial w}{\partial u}
∂
u
∂
w
has
v
v
v
in it?
0
1
2
3
4
I don't know
Check Submission
More Chain Rule Questions:
Practice: Chain Rule
Write the chain rule for
∂
z
∂
u
\frac{\partial z}{\partial u}
∂
u
∂
z
if
z
=
f
(
x
,
y
,
u
,
v
)
,
x
=
x
(
u
,
v
)
z = f (x, y, u, v),\ x = x(u, v)
z
=
f
(
x
,
y
,
u
,
v
)
,
x
=
x
(
u
,
v
)
and
y
=
y
(
u
,
v
)
.
y = y(u, v).
y
=
y
(
u
,
v
)
.
Practice: Chain Rule
Write the chain rule for
∂
z
∂
u
\frac{\partial z}{\partial u}
∂
u
∂
z
if
z
=
f
(
x
,
y
,
u
,
v
)
,
x
=
x
(
u
,
v
)
z = f (x, y, u, v),\ x = x(u, v)
z
=
f
(
x
,
y
,
u
,
v
)
,
x
=
x
(
u
,
v
)
and
y
=
y
(
u
,
v
)
.
y = y(u, v).
y
=
y
(
u
,
v
)
.
Practice: Chain Rule
Write the chain rule for
∂
z
∂
u
\frac{\partial z}{\partial u}
∂
u
∂
z
if
z
=
f
(
x
,
y
,
u
,
v
)
,
x
=
x
(
u
,
v
)
z = f (x, y, u, v),\ x = x(u, v)
z
=
f
(
x
,
y
,
u
,
v
)
,
x
=
x
(
u
,
v
)
and
y
=
y
(
u
,
v
)
.
y = y(u, v).
y
=
y
(
u
,
v
)
.
Practice: Chain Rule
Write the chain rule for
∂
z
∂
u
\frac{\partial z}{\partial u}
∂
u
∂
z
if
z
=
f
(
x
,
y
,
u
,
v
)
,
x
=
x
(
u
,
v
)
z = f (x, y, u, v),\ x = x(u, v)
z
=
f
(
x
,
y
,
u
,
v
)
,
x
=
x
(
u
,
v
)
and
y
=
y
(
u
,
v
)
.
y = y(u, v).
y
=
y
(
u
,
v
)
.
Practice: Chain Rule (1)
Consider the surface
F
(
x
,
y
,
z
)
=
e
x
2
+
y
2
+
z
2
−
(
x
2
+
y
2
+
z
2
)
=
0.
Find
∂
z
∂
x
&
∂
z
∂
y
.
F(x,~y,~z)=e^{x^2+y^2+z^2}-(x^2+y^2+z^2)=0.~~\text{Find}~\frac{\partial{z}}{\partial{x}}~\&~\frac{\partial{z}}{\partial{y}}.
F
(
x
,
y
,
z
)
=
e
x
2
+
y
2
+
z
2
−
(
x
2
+
y
2
+
z
2
)
=
0.
Find
∂
x
∂
z
&
∂
y
∂
z
.